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Impediment to Torsion from Spectral Geometry
Phys. Rev. Lett. 134, 231501 – Published 10 June, 2025
DOI: https://doi.org/10.1103/drdl-l2mp
Abstract
Modifications of standard general relativity that bring torsion into the game have a long-standing history. However, no convincing arguments exist for or against its presence in physically acceptable gravity models. In this Letter, we provide an argument based on spectral geometry (using methods of pseudodifferential calculus) that suggests that the torsion shall be excluded from the consideration. We demonstrate that there is no well-defined functional extending to the torsion-full case of the spectral formulation of the Einstein tensor.
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We recently became aware of a structurally similar result in Ref. [16]; however, the exact values of the coefficients presented therein are inconsistent with our result.
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We remark that allowed perturbations of the Dirac operator for which the term vanishes identically include gauge perturbations, where is a one-form.
More precisely, this shows that the antisymmetric part of the torsion has to vanish. The vectorial part must also be trivial due to the self-adjointness of the Dirac operator. Cartan torsion can potentially be allowed as being completely transparent in this approach.
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